The Twins Paradox: A Controversial Truth or a Perplexing Paradox?

[cire]

the twins paradox

It is true that the one that traveled is younger, is this a fact or it is a paradox

 

[christinono]

Einstein's theory of time dilation has been somewhat proven.
The website: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html
says that:

In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.C., they had gained about 0.15 microseconds compared to the ground based clock.

 

[Fredrik]

It's a fact, and not a paradox. If you'd like to know more, I suggest you use the search feature to find other threads about the twin paradox. There's about a gazillion of them.

 

[JesseM]

It depends what you mean by "the one who travelled". If both travel away from each other at constant velocity, so there's no acceleration involved, each one says the other is younger in his own reference frame, but unless one of them changes velocity they'll just get farther and farther apart, so they won't be able to get together to compare their ages in one spot. If one of them does change velocity so that they eventually meet up again, then the one that changed velocity will be the one who's younger when they meet.

 

[NeutronStar]

It is true that the one that traveled is younger, is this a fact or it is a paradox

The word "paradox" is kind of a hang-over from the days of classical physics. In purely classical terms it's a paradox because it was believe that time was absolute and therefore it would be a paradox to conclude that someone could pass through more or less time than someone else.

However, since that time we've come to realize via experiment that the conclusions of relativity are ontologically correct. In other words, it is possible for someone to pass through more or less time than someone else. This has been precisely verified in countless experiments. In literally billions of experiments actually if we count the experiments that take place in particle accelerators which we most certainly should include. The lifetime of sub-atomic particles is affected for the very same reason that the lifetime of the twins is affected in "The Twin Brothers Paradox" thought-experiment or "gedanken-experiment" as it's called in German.

The name of this thought-experiment was never changed from it's original name which includes the word paradox. But time dilation is no longer considered to be a paradox. It's now understood to be an actual property of nature. The old Newtonian concept of absolute time is now known to be ontologically incorrect.

So don't take the word paradox literally in this case. It's really not considered to be a paradox any longer. The word in this context is just a historical hangover.

 

[umbrios]

In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, each circuit taking about three days. They carried with them four cesium beam atomic clocks. When they returned and compared their clocks with the clock of the Observatory in Washington, D.C., they had gained about 0.15 microseconds compared to the ground based clock.

didn't they also put one on the space shuttle to test what the effects of gravity on time were? i think i remember hearing it somewhere.

 

[yogi]

Yep - a good example of both of these effects can be found in how GPS clocks are preset before launch - There is one correction to account for the velocity of the satellite clocks relative to the non-rotating Earth centered reference, and there is a second correction to account for the altitude of the satellite(s) relative to the surface of the earth. The velocity correction is opposite to the height correction - and the latter is much larger. Once in orbit, they keep almost perfect time with the Earth stations - small period corrections being required to adjust for the fact the orbits are not perfect.

 

[JesseM]

The word "paradox" is kind of a hang-over from the days of classical physics. In purely classical terms it's a paradox because it was believe that time was absolute and therefore it would be a paradox to conclude that someone could pass through more or less time than someone else.

That isn't generally why people call it a "paradox". The reason people call it a paradox is because they mistakenly think that relativity says the laws of nature work the same in *all* reference frames, not just inertial ones, so they imagine that the situation is completely symmetrical, since from the traveling twin's point of view the Earth moved away for a while and then turned around and moved back towards him. If the situation was indeed symmetrical, it would seem to be a paradox because each should predict the other ages slower, and both points of view would be equally valid. But since the principle of relativity only applies to inertial frames in SR, it isn't really symmetrical, so there's no paradox in the fact that one has objectively aged less when they meet up.

 

[yogi]

But JesseM - they guy who takes off from Earth doesn't really have to turn around - he can go to a distant place that is 5 LY away as measured by Earth equipment and send a message when he arrives saying: "I am here now and my clock only reads 3 years more than the day I left."

 

[JesseM]

But JesseM - they guy who takes off from Earth doesn't really have to turn around - he can go to a distant place that is 5 LY away as measured by Earth equipment and send a message when he arrives saying: "I am here now and my clock only reads 3 years more than the day I left."

Well, it will definitely take more than 10 years for the Earth to get this message, as measured by earth-clocks. And if there was a satellite moving in such a way that it was at rest relative to the traveling twin, and 5 LY behind him according to his own measurements, then when this satellite passed by the earth, the Earth could send a message saying "the satellite just passed by us and our clock reads only 3 years more than the day you left". Without either one changing velocities the situation must be symmetrical in this way.

 

[jtbell]

In 1971, experimenters from the U.S. Naval Observatory undertook an experiment to test time dilation . They made airline flights around the world in both directions, [...]

For a more recent example of this sort of thing, comparing clocks in airplanes flying around in circles to clocks on the ground, see

"Timekeeping and Time Dissemination in a Distributed Space-Based Clock Ensemble" (from a conference in 2002)

http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf

in particular the "Flight Tests" section.

 

[cire]

I don't understand this, I always thought it in this way:
there is one clock in S and another in S' if we measure the time from S to the clock at S' we get time contraction, but if we are sitting in S' and measure the time at the clock there there is not time contraction. Therefore I always thought that the twin that made the trip is equal biologically old to the one that stayed in Earth because the aging occur in the the frame you are. Of course if you try to measure the time at S' from S there is time contraction.

thanks in advance

 

[russ_watters]

But JesseM - they guy who takes off from Earth doesn't really have to turn around - he can go to a distant place that is 5 LY away as measured by Earth equipment and send a message when he arrives saying: "I am here now and my clock only reads 3 years more than the day I left."

He has to stop when he gets there though.

 

[JesseM]

He has to stop when he gets there though.

That's not relevant, he could just send a message the moment he passes next to the planet (if you idealize both the planet and the traveller as point-sized, there can be a moment when his position exactly coincides with the planet).

 

[JesseM]

I don't understand this, I always thought it in this way:
there is one clock in S and another in S' if we measure the time from S to the clock at S' we get time contraction, but if we are sitting in S' and measure the time at the clock there there is not time contraction.

S will see the clock at S' slowed down, but likewise S' will see the clock at S slowed down. The key thing to understand is that different frames define simultaneity differently, so S may say his clock read 10:00 "at the same time" that the clock at S' reads 8:00, while S' may say his clock reads 8:00 "at the same time" that the clock at S reads 5:00. And when the traveling twin switches from heading away from the Earth to heading back towards it, his definition of simultaneity changes too, so he will go from thinking the Earth clock is way behind his own to thinking it is way ahead of his own. As he returns to earth, he will still say the earth-clock is running slower than his own, but since it started out far ahead of his own when he turned around and began to return, it will still be ahead of his own when he reaches earth. So, even though the earth-clock was running slow from his point of view during both the outbound leg of the trip and the inbound leg, he will still agree with the earth-twin's prediction that his clock will be behind the earth-clock when he returns, because his plane of simultaneity swung around this way when he turned around.

This page has a diagram which may be helpful, with the vertical line representing the worldine of the earth-twin A, the bent line representing the outbound and inbound legs of the traveling twin B's worldline, and the red lines representing B's definition of simultaneity at different moments on his trip.

 

[yogi]

Russ and Jessie - Quite right Jessie - the traveler doesn't have to slow down - he can send the message on the fly - and when it is received 5 years later by the stay at home on earth, he will be older of course by 5 years plus the time it took the traveler to make the journey as measured in the Earth frame - but all that is irrelevant to the discussion - what is of consequence is that we can make a comparison of the time accumulated in the frame of the traveler with the time accumulated in the frame of the stay at home w/o having to postulate acceleration, or changing frames. It is a direct consequence of the invariance of the interval. It is the high speed particle experiment - the one why twin excursion - whatever you want to call it.

 

[JesseM]

what is of consequence is that we can make a comparison of the time accumulated in the frame of the traveler with the time accumulated in the frame of the stay at home w/o having to postulate acceleration, or changing frames.

Time accumulated between what two events? The two frames will disagree about simultaneity, so if neither changes frames, both will say the other twin aged less over a given time interval.

 

[yogi]

Jessie--There are two events - the starting point which is an event measured by twin 1 and twin 2 each in their own frame, and the ending point which is an event measured by twin 1 and twin 2 each in their own frame -- since each twin only measures time and distance in their own frame (the stay at home measures proper time and proper distance in the Earth frame and the traveler measures proper time using the clock which accompanies him) - the spacetime interval according to SR must be the same (invariant). There is never any need for either twin to make any measurement in the other twins frame therefore there is no simultaneity confusion

 

[JesseM]

Jessie--There are two events - the starting point which is an event measured by twin 1 and twin 2 each in their own frame, and the ending point which is an event measured by twin 1 and twin 2 each in their own frame

Whose "ending point"? Each twin sees himself at rest and the other in motion, so it makes just as much sense to define the ending point as the moment the traveling twin passes a planet which is at rest relative to the Earth as it does to define it as the moment the Earth twin passes a satellite which is at rest relative to the traveling twin.

-- since each twin only measures time and distance in their own frame (the stay at home measures proper time and proper distance in the Earth frame and the traveler measures proper time using the clock which accompanies him) - the spacetime interval according to SR must be the same (invariant). There is never any need for either twin to make any measurement in the other twins frame therefore there is no simultaneity confusion

Yes, of course it's true that if you just want to measure the spacetime interval/proper time between two events, there will be no disagreement between observers on this. But the traveling twin's proper time between departing the Earth and passing the planet is the same as the Earth twin's proper time between departing the traveling twin and passing the satellite (assuming, as I did before, that the distance to the planet in the Earth's rest frame is equal to the distance to the satellite in the traveling twin's rest frame). And whichever twin you pick to measure the proper time between two points on his worldline, the other twin will say this time is less than his own coordinate time between those two points. So do you agree that if neither twin changes velocity, the situation is completely symmetrical in every way?

 

[yogi]

Jessie - It is true, that if you introduce a satellite that is spaced 5LY away in the traveling twins frame, there is symmetry by definition because neither frame can tell which is in motion - but what is of moment in the present proposition is the relationship between the proper time logged by two clocks in relative motion where one clock does not have a spatial component in its interval and the other one does - Let us simply say that at a time that both twins agree upon, the traveler takes off at 0.8c and heads toward a planet 5 LY away as measured in the Earth frame. When the traveler arrives at the planet, he sends a message to his Earth twin telling him how much time has passed on his pocket watch which he carried with him. What will he transmit?

 

[JesseM]

Yes, in this situation the traveling twin will see the distance as only 3 light years, and so if he's going at 0.8c he will see the time as 3/0.8 = 3.75 years. But in his frame, it is the Earth clocks which are running slow, so at the moment he passes the planet even less then 3.75 years have passed on Earth from his point of view--he would say that the Earth clocks have only ticked forward 2.25 years at that moment. But since the earth-twin defines simultaneity differently in his own frame, he will say that at the moment the other twin passes the planet, his clocks have ticked forward by 6.25 years. Again, the "paradox" in the twin paradox really depends on the idea of the two twins meeting up again to compare clocks in the same location--only then does there have to be an objective truth about whose clock really elapsed less time.

(by the way, my name is spelled Jesse rather than Jessie--Jessie is short for Jessica)

 

[yogi]

JESSIE - stop with the first sentence - all the rest is based upon non-proper observations - not real measurements - and that is why relativity weasels out of the issue of time dilation in the one way traveler.

So we have the traveling twin reading 3.75 years on his watch. And we also know that the stay at home twin will have accumulated some time on his earthclock. The signal will take 5 years to be received, and the stay at home twin knows that the proper distance is 5LY which his brother traveled at 0.8c, so the proper time accumulated in the earth-planet frame is 5/0.8 = 6.25 years. Add this to the 5 years in transmission and the Earth bound twin should receive a signal in 11.25 years - and since he knows the transmission transit time (5 years) he then can say - my brother's clock ran slower - since he took that long trip he has remained younger than me by 2.5 years.

 

[JesseM]

JESSIE

I just told you, my name is spelled "Jesse", not "Jessie".

- stop with the first sentence - all the rest is based upon non-proper observations - not real measurements - and that is why relativity weasels out of the issue of time dilation in the one way traveler.

All of relativity is based on what you'd find if you performed a certain "real measurement". Simultaneity, for example, is based on the idea that each observer synchronizes spatially separated clocks by using the assumption that light travels at the same speed in all directions relative to themself. If the traveling twin is riding on the front end of a giant spaceship 3 lightyears long, and he synchronizes his clock with the clock at the ship's back end by sending a light-pulse out from the midpoint of the ship and making sure the clocks on both ends read the same time at the moment the light reaches them, then at the moment the back end passes the Earth the clock on the back end will read 3.75 years (the same time his own clock reads when he passes the planet), but at that moment the earth-clock will only read 2.25 years. So when he says only 2.25 years have passed on Earth at the time he passes the planet, this is based on perfectly real measurements. Likewise, if the planet is at rest relative to the earth, then the planet's clock and the Earth's clock can also be synchronized by sending a light pulse from the midpoint of the line between them, and making sure that both the clock on Earth and the clock on the planet read the same time when the light reaches them. In this case, when the traveling twin passes the planet, the clock on the planet will read 6.25 years.

So we have the traveling twin reading 3.75 years on his watch. And we also know that the stay at home twin will have accumulated some time on his earthclock. The signal will take 5 years to be received, and the stay at home twin knows that the proper distance is 5LY

There is no such thing as "proper distance", you just mean the distance in his own coordinate system.

which his brother traveled at 0.8c, so the proper time accumulated in the earth-planet frame is 5/0.8 = 6.25 years. Add this to the 5 years in transmission and the Earth bound twin should receive a signal in 11.25 years - and since he knows the transmission transit time (5 years) he then can say - my brother's clock ran slower - since he took that long trip he has remained younger than me by 2.5 years.

Yes, but now suppose the Earth sends a signal in the direction of the traveling twin when the earth-clock reads 2.25 years, at which point the Earth will be a distance of 3 light years away in the twin's frame. With a few modifications, the exact same argument you made can be used to look at this from the traveling twin's perspective:

So we have the Earth twin reading 2.25 years on his watch. And we also know that the traveling twin will have accumulated some time on his clock. The signal will take 3 years to be received, and the traveling twin knows that the distance in his coordinate system is 3LY which his brother traveled at 0.8c, so the proper time accumulated in the traveling twin frame is 3/0.8 = 3.75 years. Add this to the 3 years in transmission and the traveling twin should receive a signal in 6.75 years - and since he knows the transmission transit time (3 years) he then can say - my brother's clock ran slower - since he took that long trip he has remained younger than me by 1.5 years.

 

[yogi]

ok Jessica - the Earth clock will not read 2.25 years when the traveler (whether it be the front end reaching the planet or the back end reaching earth) completes the journey. The arrival event cannot take less than 5 years in the Earth frame even if the traveler moves at c - and since he only moves at 0.8c the arrival event will correspond with an Earth clock reading of 6.25 years. Your 2.25 years is a good example of jumping back and forth between what is measured in a frame by a comoving observer what how fast the clock appears to run when it is measured as it passes between two clocks in another frame.

Also - there is certainly a proper distance - the term is used by many authors when referring to a distance measured in the frame of the observer.

I would also disagree that all of relativity is based upon "real measurement" Maybe it should be - and if it were these differences in interpretation would not arise - take a look at Einstein's 1905 paper again ... three times he parenthetically emphasizes ... (as observed in the other frame). Then w/o justification he uses the apparent observations to arrive at real time dilation - As I have said many times on this board..only apparent observations as to how fast time passes in the other frame can be considered reciprocal - real time differences occur, but they cannot be reciprocal ..If between two spacetime events, a clock in a first frame accumulates more time than a clock in a second frame, then the clock in the second frame must accumlate less time than the clock in the first frame. Einstein was never able to explain this .. by 1912 he was certain the twin aging problem had nothing to do with acceleration .. but he still didn't address the problem with a positive explanation... only a negative comment that eliminated turn around acceleration as the culprit.

I know your name is Jesse - I am just twisting your tail.

 

[Hurkyl]

The arrival event cannot take less than 5 years in the Earth frame even if the traveler moves at c - and since he only moves at 0.8c the arrival event will correspond with an Earth clock reading of 6.25 years.

You're still falling prey to absolute simultaneity.

 

[russ_watters]

Russ and Jessie - Quite right Jessie - the traveler doesn't have to slow down - he can send the message on the fly...

This is why these conversations annoy me: it started with the twins paradox and morphed into various other scenarios. By constantly changing the scenario, you can confuse an otherwise relatively simple question. In the twins paradox, the accelerations are what tell you which twin is moving. In Jesse's first post he said

It depends what you mean by "the one who travelled". If both travel away from each other at constant velocity, so there's no acceleration involved

Well, that's not the twins paradox anymore. Then you proposed a third scenario:

But JesseM - they guy who takes off from Earth doesn't really have to turn around

which involves an acceleration at the beginning (taking off from earth), but then not at the end. I was wrong to say he needed to stop - he doesn't, you already know he's the one moving because he "took off". In Jesse's scenario, which sounds like two ships, you need some way to figure out which one is moving. If it really is just two ships from distant planets who have never met but cross paths, the situation really is symmetrical - until you start defining "stationary" things like planets to reference their movement from.

And then there's that pesky simultenaity bit, which is why I prefer the twins paradox as Einstein defined it, since it doesn't involve simultenaity issues: the twins are standing next to each other at the start and end of the scenario.

 

[JesseM]

the Earth clock will not read 2.25 years when the traveler (whether it be the front end reaching the planet or the back end reaching earth) completes the journey.

Well, if you're asking what the Earth clock reads "at the same time" that the traveling twin reaches the planet, then the answer will be different depending on your reference frame. So let's just focus on the reading on the clock at the back of the ship at the moment it passes the earth. Remember, the traveling twin "synchronized" the clock at the front with the clock at the back based on the assumption that light travels at c in all directions relative to himself. So, he just sent out a light pulse from the midpoint of the ship, and made sure that both clocks read the same time at the moment the light hit them. But from the point of view of the earth, this procedure will not result in the two clocks being synchronized. From the Earth's point of view, light travels at c in all directions relative to the earth, so since the back end of the ship was moving towards the point where the light pulse was emitted, and the front end was moving away from the point where it was emitted, this means the light will hit the back end before the front end, and thus the traveling twin's "synchronization" procedure will result in the clock at the back end being ahead of the clock at the front end, from the Earth's point of view. In this case, if the ship appears 1.8 light-years long in the Earth's frame (so that it is 3 light-years long in the ship's own rest frame, and thus in the ship's frame the back end passes the Earth at the same moment the front end passes the distant planet), then the clock at the back end will always appear 2.4 years ahead of the clock at the front end. The back end will take 1.8/0.8=2.25 years to reach the Earth's position in the earth-frame, and it will have ticked forward by 2.25*0.6=1.35 years in that time, so the total time it will read at the moment it passes the Earth is 1.35+2.4=3.75 years, which of course is the same time that the clock at the front end reads at the moment it passes the planet. So by the ship's definition of "same moment", the front end passed the planet at the "same moment" that the back end passed the earth, and both frames agree that when the back end passed the earth, the clock on the back end read 3.75 years while the clock on Earth read 2.25 years.

The arrival event cannot take less than 5 years in the Earth frame even if the traveler moves at c

Of course that's true, the key words being "in the Earth frame".

and since he only moves at 0.8c the arrival event will correspond with an Earth clock reading of 6.25 years.

Yes, all correct. But the thing to note is that in the Earth's frame, the event of the back end passing the Earth happens well before the event of the front end passing the planet. But because the traveling twin considers the clocks on both ends to be synchronized, then in his frame both these events happened at the same time. And the situation is symmetrical, because the way the earth-observer decides what reading on his own clock corresponds to the time the distant front end of the ship reached the planet is to have another clock sitting on the planet, which he "synchronizes" with his clock on Earth using exactly the same light-pulse method that the traveling twin used, except that he assumes light travels at the same speed in both directions relative to himself (which means from the traveling twin's point of view, the clock on the planet is ahead of the clock on Earth by 4 years). This is what I meant by saying all of relativity is based on "real measurements", it's all based on noting the times on clocks next to each event.

Also - there is certainly a proper distance - the term is used by many authors when referring to a distance measured in the frame of the observer.

I've never heard this term, but I googled it and you're right that some people use it. It seems like confusing terminology, because "proper time" is a time interval as measured by an observer, even an accelerating one, whereas this definition of "proper distance" just means length as measured in an inertial observer's reference frame, so it doesn't really seem analogous to proper time.

It does seem like the term is used more rarely--googling "proper time" + relativity gives 33,800 hits, while googling "proper distance" + relativity only gives 5,100 hits.

I would also disagree that all of relativity is based upon "real measurement"

Well, see above. 2.25 years is the time the earth-clock reads when the back end of the ship passes the earth, and at that moment the clock on the back end reads 3.75 years, just as the clock on the front end reads 3.75 years as it passes the planet. And these two clocks were synchronized by the traveller based on the assumption that light travels at speed c in all directions in his own frame, so if you send a light pulse from the midpoint of the ship, both clocks should read the same time at the moment the light hits them.

Maybe it should be - and if it were these differences in interpretation would not arise - take a look at Einstein's 1905 paper again ... three times he parenthetically emphasizes ... (as observed in the other frame). Then w/o justification he uses the apparent observations to arrive at real time dilation - As I have said many times on this board..only apparent observations as to how fast time passes in the other frame can be considered reciprocal - real time differences occur, but they cannot be reciprocal ..If between two spacetime events, a clock in a first frame accumulates more time than a clock in a second frame, then the clock in the second frame must accumlate less time than the clock in the first frame.

You are not taking into account the physical procedure Einstein gave for how each observer should "synchronize" clocks at different locations which are at rest in his own frame. Once you do this, you get the relativity of simultaneity, and you understand how each observer can measure the other observer's clocks to be running slower than his own. The question of whose clock is "really" running slower is not physically meaningful unless you can think up a physical procedure to decide whose clocks are "really" synchronized, but all the evidence points to the fact that no experiment will pick out a preferred reference frame.

 

[yogi]

Russ - Jesse - I am attempting to reduce the twin problem to two different excursions - first we consider the outbound journey - so since we have about 10 million words already written about why the clock paradox is not really a paradox and about 5 million that still claim it is - I am attempting to pin down things using only proper measurements. We will take the case of the traveler - jesse - you start off immediately by making an improper measurement - you first calculate the contracted distance based upon how the traveler views the 5ly in the Earth frame and from there you figure the time lapse in the traveling twins frame - in actuality - the traveling twin can only make one proper measurement - he has only one clock and he can only read that in his own frame - and based upon his reading at the start and arrival (the time accumulated from when the two twins were together and the time when the traveler reaches the distant planet that is 5ly distant in the Earth frame). You like all relativist want to slide back and forth between the two frames to save reciprocity...but Contraction is not a real thing - it is calculated consequent to time dilation - the proper reading on the travelers clock gives a permanent number that will be there after the motion stops - you can use that to calculate what the traveler would mistakently believe to be the distance to the planet - but that is a non proper measurement - one calculated from the travelers own clock that he reads at the end of the trip time - take a look at ResnicK - "Introduction of SR" Of course you can come back and say "contraction is real" - and I will say who says so - then we can each quote the great defenders of relativity theory and get remarkably different answers like that given by Eddington: "The contraction is true, but its not really true"

Keep it simple - the traveler reads his clock when the two twins are together - they can be flying past each other or in the same reference system. Whatever - there will be some start time on his watch - and upon arrival the traveler will read a different time on this same watch. This is his proper time lapse in the only frame he can make a proper reading - in the Earth frame there can be two clocks - one at the Earth and one on the planet - or if you don't like that, the traveler can send a radio signal back to Earth informing the stay at home twin what his clock reads as he passes the planet - in which case there is only one clock in the Earth frame and one watch in the travelers frame. Morover, we can substitute a high speed muon for the traveler and specify that it travels so fast it just reaches the planet as it decays - we know the decay time of the muon to be on average about 2 usec in its own frame. ..the proper time in the traveling frame is therefore 2usec - in the Earth frame the time is much greater (about 5 years). The invariance of the interval guarantees that the clock in the muon frame runs at a different rate than the clock in the Earth frame - there are no observations of improper temporal or spatial elements - everything is measured by the two twins each in their own frame. We are therefore forced to conclude either - that the two twins age at different rates even though neither has turned around, or they have somehow both aged the same during the muons flight to a distant planet. Which?

 

[cire]

I'm taking ED II using jackson I made the homework etc.. but I don't fully understand this I originally posted the question about the twins paradox trying to understand it... and got immersed in disccussions that doesn't clarify me
on the other hand I think that the c at the lorentz transformation is not the velocity of light is the velocity of a massless particle of an true vacuum or "the maximum speed possible" or "the limit speed", what happens is that the mass of the photon is so light that its velocity (orthe velocity of the em wave) is close to this "maximun nature velocity", what do you guys think?

 

[yogi]

Cire - The parties to this discussion all seem to agree that clocks run at different speeds when they are in relative motion - what is being considered is whether it is necessary to have one of them turn around and return to the starting point in order to measure the age difference.